Golden Balls: Taking Advantage of Tit-for-Tat

A few years back I shared a clip from a popular British game show, Golden Balls, which illustrates in an entertaining way game theory and the prisoner’s dilemma. Today I want to share another clip from the same show to explore another aspect of game theory: tit-for-tat.

Tit-for-tat is a common term used in game theory. The concept was first introduced as a strategy by Anatol Rapoport in two game theory tournaments conducted by Robert Axelrod that were held around 1980. Tit-for-tat goes like this: a person will first cooperate, then subsequently replicate an opponent’s previous action. If the opponent previously was cooperative, the agent is cooperative; if not, the other person is not. Think of it an eye for an eye, a tooth for tooth. If I screw you over, I should expect you to screw me over. If I am nice to you, it’s common to get a nice response back.

, as shown in the Golden Balls “steal or split” clip below, with players going for a jackpot worth more than £100,000. If Steven and Sarah both choose the “split” ball they share the jackpot; if they both choose to “steal”, they get nothing; if one goes for “split” and the other chooses “steal”, then the stealer gets the entire jackpot.

Here’s what happened:

On the surface it looks like they will cooperate. Steven promised Sarah with high passion that he would choose the split ball so they could share the prize. Sarah appears to sincerely agree on the split strategy, saying that “everyone who knew me would just be disgusted if I stole.” The cooperative tit for tat strategy was in place—until suddenly it wasn’t.

But even though Steven said it was an “easy decision,” he should have known things might go awry, since he had “stolen” from Sarah in previous rounds. Yep, Sarah did the predictable and “stole” from Steven when the stakes were highest.

The crestfallen Steven said, “Some people look for revenge quite easily, and greed knows no bounds.” But Steven should have known his greed would come back to haunt him; Sarah surely wasn’t going to roll over. As she said, “Having been stabbed in the back last time, I just couldn’t put myself through it again.”